S. Poljak and Zs. Tuza, The Expected Relative Error of the Polyhedral Approximation of the Max-Cut Problem, Operations Research Letters 16 (1994) 191-198.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....no K 5 minor. In this paper we will mainly be concerned with random graphs. In what follows, G n;p denotes a graph on n vertices, whose edges are chosen randomly and independently with probability p, 0 p 1. We denote by opt(G n;p ) the cardinality of the max cut for this graph. Poljak and Tuza [13] have obtained the following results for random graphs. Theorem 1.1 (Dense Graphs) Let p = p(n) be a function such that 0 p 1 and p(n) log n=n) Then the integrality ratio as n 1 with probability 1 o(1) Theorem 1.2 (Sparse Graphs) Let p = p(n) be a function such that 0 p 1, ....

....we can combine this with Lemma 3.1 to obtain (1 o(1) as n 1, with probability 1 o(1) 4 Dense Graphs In this section we prove that random dense graphs have asymptotically the same integrality ratio as complete graphs. Our proof is modelled along the lines of that of Poljak and Tuza [13] for Theorem 1.1. Lemma 4.1 (Cherno Inequality [4] Let X 1 ; X 2 ; X n be independent Bernoulli trials with Pr[X i = 1] p, 0 p 1. Then if X is the sum of the X i and if is E[X] for any 0, Pr[j Xj n ] e n 2 2p(1 p) De nition 4.1 (Uniform Cover) For any odd integer k ....

S. Poljak and Zs. Tuza, The Expected Relative Error of the Polyhedral Approximation of the Max-Cut Problem, Operations Research Letters 16 (1994) 191-198.

.... experiments based on polyhedral approaches are given in [2, 3, 14] It turns out that almost planar graphs can be handled efficiently for quite large jV j: Graphs on up to 2501 nodes and 7500 edges are dealt with in [4] On the other hand it becomes clear from probabilistic arguments [15, 16] that the polyhedral approach is unlikely to be successful on moderately dense graphs of even modest size. This can also be seen in [3, 6] From these papers it becomes clear that random problems with 50 nodes and edge probability 1 2, or problems with 100 nodes and edge probability 3 10 are not ....

S. POLJAK and Zs. TUZA. On the expected relative error of the polyhedral approximation of the max-cut. Technical Report Report 92757-OR, Institut fur Diskrete Mathematik, Universtitat Bonn, 1992.

....5 ) 1:131. The conjecture was almost confirmed by the result of Goemans and Williamson [GW94] who proved (G; w) mc(G;w) 1:138 for any graph G and any nonnegative edge weights w. b) Relaxation by the metric polytope MET Sigma1 n Thetan . The performance of (G) mc(G) was studied in [PT92]. In particular, it has been shown that lim n 1 (G n;pn ) mc(G n;pn ) Gamma 2 (with probability 1 Gamma o(1) for certain edge probabilities p n , p n 0. This means that the metric approximation (G) can be as bad as possible, since the same worst case ratio is attained by jE(G)j=mc(G) On ....

S. Poljak and Zs. Tuza. On the expected relative error of the polyhedral approximation of the max-cut, Operations Research Letters, 16:191--198, 1994.

No context found.

S. POLJAK and Zs. TUZA. On the expected relative error of the polyhedral approximation of the max-cut. Operations Research Letters, 16: 191--198, 1994.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC